LI Kang-Ning YANG Chuan-Lu WANG Mei-Shan MA Xiao-Guang



Geometry, Electronic Properties and Magnetism of BeO(3, 4, 5) Clusters①

LI Kang-Ning YANG Chuan-Lu②WANG Mei-Shan MA Xiao-Guang

(264025)

Thirty BeO(3, 4, 5) stable isomers are obtained with optimization and frequency analysis based on density functional theory and all-electron numerical basis set. The hundreds of initial geometries are built using the “binomial” scheme. The binding energies, the energy gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, and the magnetic moments of all stable isomers are calculated and analyzed. It is found that the Be–O bonds play an important role in the stability of the clusters, and the total magnetic moments of the isomers mainly depend on the magnetic moment of O atoms, Be atoms and the arrangement of magnetic moments of all atoms.

BeOclusters, Be–O bond, binding energy, magnetism;

1 INTRODUCTION

Beryllium oxide is a rare oxide, which can be used in high resistance and high thermal con- ductivity of ceramic materials. Besides, beryllium and beryllium oxides are indispensable valuable materials in the atomic energy, rockets, missiles, aviation, and metallurgical industry. Ren. have studied the geometric and electronic properties of BeO clusters[1], such as the binding energy, stability and aromaticity as well as their key features[2]. The structures of (BeO)clusters (= 2～12, 16, 20, and 24) were studied by using the method of combining the genetic algorithm with density function theory. The global minimum structures of (BeO)clusters are rings up to= 5, double rings at= 6 and 7 and cages at≥8[1]. The theoretical calculations have been carried out to investigate the (BeO)(2～9) clusters with emphasis on their polarizability per atom, differential polarizability[3-6]per unit, and polarizability anisotropy. Boldyrev. have calculated the molecular properties of BeOBe molecule, such as bond length and total energy[7]; and localized stationary points on the B3LYP/cc-pVDZ energy hyper surfaces of Be2O2have been studied by Srnec[8].

However, all the investigations are mainly focused on studying the geometrical and electronic structures of clusters, which have equal numbers of Be and O, and more complex clusters containing different numbers of Be and O atoms have not yet been reported, which limits to systematically unders- tand, prepare, and apply the clusters, including Be and O atoms. Especially, for catalytic applications, one can choose appropriate clusters dependent on understanding the characteristics of various isomers. In this article, we focus on the geometry, electronic properties and magnetism of clusters, including both the same and different ratios of Be and O atoms in order to fill the gap of the investigations for the BeO(+3, 4, 5) clusters.

2 COMPUTATIONAL DETAILS

In the process of looking for isomers, the suitable initial structures are a key point. The possible structures for the clusters containing several ele- ments are much more complex than those of the single element. The construction of the initial structure is very important, but no regular scheme. One must balance the diversity of possible structures and the consuming time of reckoning. When the total number of atoms is not too much, binomial scheme suggested by Ryzhkov.[9]is a very effective method. For the five atomic clusters with two elements, this scheme is shown in Fig. 1. One can firstly optimize the BeO stable structure, and form Be2O and BeO2clusters with BeO stable structure by adding a Be or O atom, respectively. When the stable isomers of Be2O and BeO2are obtained, one can add a Be or O atom to make the initial structures of BeO3Be2O2and Be3O clusters, respectively. The initial structures of Be4O, Be3O2, Be2O3and BeO4clusters can also be constructed in the same way. It should be noted that different positions of the adding atom will result many different structures, and some of them can reduce to a same stable structure. Therefore, the choice of the position is not trivial. The optimized structures are accompanied with the calculations of vibration frequency to confirm the energy stability. Finally, the electronic properties of the stable isomers are calculated and analyzed.

All the calculations are performed with the generalized gradient approximation PW91[10, 11]with basis set DNP based on density functional theory (DFT), which is implemented in Dmol3module[12]of Material Studio 5.5. The standard self-consistent energy convergence in the calculation is 1.0×10-6Hartree. Max force is 5.0×10-4Hartree/Bohr. Max displacement is 0.002 Å. In order to accelerate convergence, the smearing is used in the calculation with the standard to be 0. 005 Hartree.

Fig. 1. Scheme for building initial structures of BeO(3, 4, 5) clusters

3 RESULTS AND DISCUSSION

3. 1 Stable geometric structures

According to binomial scheme, we have built the initial structures of BeO(3, 4, 5), and obtained stable structures with optimization calcula- tions. The energy stability of all structures has been confirmed because no imaginary frequency has been found. For BeO(3) clusters, we obtain three stable structures and show them in Fig. 2. The only one BeO2isomer is numbered as “1”, and the other two Be2O isomers as “2” and “3”, respectively.

Fig. 2. Optimized BeO(3) stable isomers (green represents the Be atom, red represents the O atom. The same hereinafter)

For BeO(4) clusters, nine stable structures are obtained from large numbers of initial configurations. As shown in Fig. 3, there are two Be3O isomers numbered as “1” and “2”, three Be2O2isomers as “3”, “4” and “5”,and four BeO3isomers as “6”, “7”, “8” and “9”, respectively. For Be2O2, these three structures are in good agreement with the conclusion of Srnecreported in literature[8].

For BeO(5) clusters, total eighteen stable structures are shown in Fig. 4, including two Be4O isomers, five Be3O2isomers, four Be2O3isomers and seven BeO4isomers. They are number- ed as from 1 to 18, respectively.

Fig. 3. Optimized BeO(4) stable isomers

Fig. 4. Optimized BeO(5) stable isomers

3. 2 Energy stability and chemical stability

Binding energy (E) is an index of the energy stability of the cluster. Therefore, we useEto evaluate the stability of the cluster. The calculation formula ofEis:

E = E(BeO) –(Be) –(O) (1)

where(BeO) is the total energies of BeO, and(Be) and(O) are the energy of single Be or O atom. The larger absolute value ofEmeans better energy stability.

The energy gap (E) between the highest occupied molecular orbital (HOMO) and the lowest unoccu- pied molecular orbital (LUMO) is an important index of the chemical activity of the cluster. The largerEmeans a more stable chemical activity of the cluster.

For BeO(3) clusters, all theE, bond length () andEof the clusters are listed in Table 1. FromEcolumn, we can find that cluster “3” has the largestE, implying it is the most energy stable one.For theand symmetry of “3”, our results are in agreement with Boldyrev’s (theof Be–O is 1.428 Å, and symmetry isD)[7].

For Be2O, the averageof Be–O for “3” is shorter than that for “2”, and theEof “3” is greater, implies that theEof the cluster is related to the length of Be–O bond. In addition, fromEcolumn, we can find that cluster “3” has the largestE, implying it is the most chemical stable one. In general, among the three clusters, “3” is the most stable one both in energy stability and chemical stability.

TheE,andgof BeO(4) clusters are listed in Table 2. We can find that “2”, “5” and “6” are the most energy stable structures corresponding to Be3O, Be2O2and BeO3. For Be3O, maximum of three Be–O bonds can be allowed; however, “2” has two Be–O bonds which are smaller than those of “1”. For Be2O2, the smallest averageof Be–O is “5” and for BeO3, among “6”, “7” and “8”,the corresponding value is “6”. Therefore, it can be concluded that theEof these clusters is closely related to theirof Be–O. FromEcolumn, we can find “2”, “5”, and “8”, corresponding to Be3O, Be2O2and BeO3, respectively, are the highest chemical stability. In general, “2” and “5” are the most stable both in energy and chemical stability. We can also find that “6” has the largestE, but itsEis only 0.883 eV, so “6” has a strong chemical activity. After examining the distribution of HOMO and LUMO orbitals, we find that the differentEmainly depend on the location of orbitals. Generally, the orbitals located on O atoms bring about smallEwhile those on Be atoms give largeE. As shown in Fig. 5, the HOMO and LUMO of isomer “6” are almost completely located on the two O atoms, which give a smallerEof 0.883 eV. However, for isomer “8”, the LUMO is almost completely located on the Be atoms, while its HOMO is located partly on the Be atoms, although there is a part of HOMO located on the O atom, which brings about a biggerEof 2.194 eV. For these nine isomers, theirEare obviously different, ranging from 0.384 to 2.736 eV, which implies that they have various chemical activities.

Table 1. Symmetry, Binding Energy (Eb), Bond Length (d), and Energy Gap (Eg) of BemOn(m + n = 3)

arepresents the Be–O bonds.brepresents the Be –Be bonds.crepresents the O–O bonds. The same hereinafter

Table 2. Symmetry, Binding Energy (Eb), Bond Length (d), and Energy Gap (Eg) of BemOn(m + n = 4)

HOMO of isomer “6”    LUMO of isomer “6”     HOMO of isomer “8”    LUMO of isomer “8”

Fig. 5. Isodensity surfaces for the HOMO and LUMO of isomers “6” and “8” (4)

For BeO(5) clusters,b,, andgare listed in Table 3. We find that “2”, “6”, “10” and “12” are the largerEcorresponding to Be4O, Be3O2, Be2O3and BeO4, respectively. Namely, they are more stable in energy. We can also find they have the shortest averageof Be–O. For Be2O3, the averageof Be–O for “10” and “11” are 1.767 and 1.594 Å, respectively, which are smaller than those of the other three clusters. For cluster “10”, the averageof Be–O is not the minimum one, but its four Be–O bonds are shorter than those of cluster “11” although the latter has six Be–O bonds.In a word,Ehas a strong relationship with theof Be–O. FromEcolumn, it can be seen that theEof BeO(5) clusters are obviously different, ranging from 0.110 to 3.198 eV. The one with the largest 3.198 eV ofEis isomer “6”. As shown in Fig. 6, for isomer “6”, the HOMO and LUMO are almost completely located on the Be atoms. For isomer “4” with the smallestEof 0.110 eV, its LUMO is located partly on O atoms, although the HOMO is still mainly on the Be atoms. The similar energy levels of the two atoms result in smallE. We also examine the HOMO and LUMO for all other isomers and find that the HOMOs for all isomers mainly locate on Be atoms, while the LUMOs locate on a small part of the orbital. However, the pictures show that both HOMO and LUMO of “6” are on the two Be atoms, implying that theEare mainly dependent on the energy levels of Be atom in the isomers. Therefore, theEis large. We find that “2”, “6”, “10” and “13”, corresponding to Be4O, Be3O2, Be2O3and BeO4, have largerE. Namely, they have more chemical stability. In a word, “2”, “6” and “10” are more stable both in energy and chemical stability. For BeO4, “12” has the biggestE, while “13” has the largestE, reaching 2.603 eV, so “13” has the most stable chemical stability.

Table 3. Binding Energy (Eb), Bond Length (d), and Energy Gap (Eg) of BemOn(m + n = 5)

3. 3 Magnetic moments

For BeO(3), magnetic moment () of each atom, totaland spin state are listed in Table 4.One can find that isomers “1” and “2” are not magnetic, and the total magnetic moment of “3” is relatively larger, reaching 1.997 μB, and the spin state is 3. After carefully checking theof each atom, we find that theof both Be atoms in “3” is not zero, and project in the same direction, resulting in the non-zero total.

For BeO(4), all theare listed in Table 5. Various totalcan be found in these clusters. All isomers of Be3O and Be2O2are not magnetic. However, the totalof BeO3is relatively large, and the largest one reaches 2.047 μB. Interestingly, unlike the case of Be2O, theof these clusters results from O atoms but not Be atoms because one can find in Table 5 that theof O atoms in this isomers project in the same direction.

Table 4. Magnetic Moment (μ), Total Magnetic Moment(μ) and Spin State of BemOn(m + n = 3)

Arepresents O magnetic moment.Brepresents Be magnetic moment (The same hereinafter)

Table 5. Magnetic Moment (μ), Total Magnetic Moment and Spin State of BemOn(m + n = 4)

Table 6 collectsof BeO(5) clusters. One can find that all isomers of Be4O and Be3O2are not magnetic, while for Be2O3, theof cluster “7” is relatively larger, reaching 1.6 μB,and the reason is that theof two O atoms and one Be atom are not only non-zero but also align along the same direction. For BeO4,of “14” and “15” are relatively larger, reaching 1.906 and 1.982 μB, respectively. Table 6 shows that not only theof O atoms but also the Be atom contribute to the total. On the whole, both O and Be atoms can lead to the non-zeroof BeO(3, 4, 5) clusters, as long as theof the atoms is properly arranged. We also find that O atoms more often contribute to the non-zero.

Table 6. Magnetic Moment (μ), Total Magnetic Moment and Spin State of BemOn(m + n = 5)

HOMO of isomer “4”    LUMO of isomer “4”    HOMO of isomer “6”    LUMO of isomer “6”

Fig. 6. Isodensity surfaces for the HOMO and LUMO of isomers “4” and “6” (5)

4 CONCLUSION

The theoretical calculations have been carried out to investigate the BeO(3, 4, 5) clusters with emphasis on their geometry, electronic properties and magnetism. Three BeO(3), nine BeO(4) and eighteen BeO(5) stable isomers are obtained with optimization calculations and frequency analysis. By analyzingEandof the clusters, we find that theEis related to theof Be–O. It is found that some isomers are non-zeroand both the magnitude and direction arrangement ofof the O and Be are responsive for the total. The presented results provide a systematical knowledge for BeO(3, 4, 5) clusters and can be guidance for future theoretical and experimental studies relative to these clusters.

(1) Ren, L.; Cheng, L.; Feng, Y.; Wang, X. Geometric and electronic structures of (BeO)(2～12, 16, 20 and 24): rings, double rings and cages.2012, 137, 014309-5.

(2) Jiao, H.; Schleyer, P.; Warmuth, R. Theoretical studies of the structure, aromaticity and magnetic properties of O-benzyne.1997, 36, 2761-2764.

(3) McLean, A. D.; Yoshimine, M. Theory of molecular polarizabilities.. 1967, 47, 1927-1935.

(4) Alipour, M. Theoretical determination of the differential polarizability and anisotropy of alkaline earth oxide nanoclusters (BeO)(= 2～9): the basis set and electron correlation effects.2014, 114, 255-260.

(5) Karamanis, P.; Xenides, D.; Leszczynski, J. Polarizability evolution on natural and artificial low dimensional binary semiconductor systems: a case study of stoichiometric aluminum phosphide semiconductor clusters.2008, 129, 094708-12.

(6) Mohammed, A. A. K.; Limacher, P. A.; Champagne, B. Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities.2013, 34, 1497-1507.

(7) Boldyrev, A. I.; Simons, J.study of the strong binding of BeO to Li, Be and B atoms in the hyper stoichiometric LiOBe, BeOBe and BeOB molecules.. 1995, 99, 15041-15045.

(8) Srnec, M.; Zahradník, R. Small group IIa–VIa clusters and related systems: a theoretical study of physical properties, reactivity and electronic spectra.. 2007, 11, 1529-1543.

(9) Ryzhkov, M. V.; Ivanovskii, A. L.; Delley, B. T. Electronic structure and geometry optimization of nanoparticles Fe2C, FeC2, Fe3C, FeC3and Fe2C2.. 2005, 404, 400-408.

(10) Perdew, J. P.; Chevary, J. A.; Vosko, S. H. Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation.1992, 46, 6671-6687.

(11) Perdew, J. P. Generalized gradient approximations for exchange and correlation: a look backward and forward.1991, 172, 1-6.

(12) Delley, B. From molecules to solids with the Dmol3approach.. 2000, 113, 7756−7764.

①This project was supported by the National Natural Science Foundation of China (Nos. NSFC-11174117 and NSFC-11374132)

.E-mail: yangchuanlu@263.net

10.14102/j.cnki.0254-5861.2011-0732

2 March 2015; accepted 60 June 2015